PPT Slide
Sharpness of the Multiplicity Function
- g(N,s) is very sharply peaked around s=0;
- we want get a more analytical form of g(N,s) when N>ɭ and s<<N
- we will follow the same procedure as for the random-walk problem!
- we use the Stirling approximation:
Width of the g(N,s) multiplicity function governed by for s/N=(1/2N)1/2 the value of g is e-1 of g(N,0)
g(N,s) is a Gaussian-like distribution!
For N>ɭ the distribution gets very sharp --> strong consequences for thermodynamic systems